• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.817-827
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• 2021

In this paper, we prove that a diffeomorphism f on a normal almost contact 3-manifold M is a CRL-transformation if and only if M is an α-Sasakian manifold. Moreover, we show that a CR-loxodrome in an α-Sasakian 3-manifold is a pseudo-Hermitian magnetic curve with a strength $q={\tilde{r}}{\eta}({\gamma}^{\prime})=(r+{\alpha}-t){\eta}({\gamma}^{\prime})$ for constant 𝜂(𝛄'). A non-geodesic CR-loxodrome is a non-Legendre slant helix. Next, we prove that let M be an α-Sasakian 3-manifold such that (∇_YS)X = 0 for vector fields Y to be orthogonal to ξ, then the Ricci tensor 𝜌 satisfies 𝜌 = 2α²g. Moreover, using the CRL-transformation $\tilde{\nabla}^t$ we fine the pseudo-Hermitian curvature $\tilde{R}$, the pseudo-Ricci tensor $\tilde{\rho}$ and the torsion tensor field $\tilde{T}^t(\tilde{S}X,Y)$.

• The Journal of Korea Robotics Society
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• v.8 no.3
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• pp.179-185
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• 2013

In this paper we propose a haptic interaction system that physically represents the underlying geometry of objects displayed in a 2D picture, i.e., a digital image. To obtain the object's geometry displayed in the picture, we estimate the physical transformation between the object plane and the image plane based on homographic information. We then calculate the rotated surface normal vector of the object's face and place it on the corresponding part in the 2D image. The purpose of this setup is to create a force that can be rendered along with the image without distorting the visual information. We evaluated the proposed haptic rendering system using a set of pictures of objects with different orientations. The experimental results show that the participants reliably identified the geometric configuration by touching the object in the picture. We conclude this paper with a set of applications.

• International Journal of CAD/CAM
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• v.9 no.1
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• pp.79-83
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• 2010

Tidal bore is a peculiar nature phenomenon which is caused by the lunar and solar gravitation. Based on the physical characters of tidal bores, in this paper we propose a novel method to model and render this phenomenon, especially the tidal waves in Qiantang estuary. According to Boltzmann equation for tidal waves, we solve it with the novel triangle mesh of Kinectic Flux Vector Splitting (KFVS) mode. Then a method combining a curve forecasting wave and particles model is proposed to render the dynamic scenes of overturning tidal waves. Finally, with some rendering technologies, various realistic tidal waves under diversified conditions is rendered in real time.

• Journal of Korea Multimedia Society
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• v.22 no.5
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• pp.580-587
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• 2019

In this paper, a plane detection method using depth information is proposed. 3-D characteristics of a pixel are defined as a direction and length of a normal vector whose is calculated from a plane consisting of a local region centered on the pixel. Image coordinates of each pixel are transformed to 3-D coordinates in order to obtain the local planes. Regions of each plane are detected by calculating similarity of the 3-D characteristics. The similarity of the characteristics consists of direction and distance similarities of normal vectors. If the similarity of the characteristics between two adjacent pixels is enough high, the two pixels are regarded as consisting of same plane. Simulation results show that the proposed method using the depth picture is more accurate for detecting plane areas than the conventional method.

• Journal of Positioning, Navigation, and Timing
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• v.7 no.3
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• pp.155-163
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• 2018

This study examined methods to enhance navigation performance and reduce the divergence of navigation solutions that may occur in the event of global positioning system (GPS) failure by integrating the GPS/inertial navigation system (INS) with the three-dimensional (3D) magnetic vector measurements of a magnetometer. A magnetic heading aiding method that employs a magnetometer has been widely used to enhance the heading performance in low-cost GPS/INS navigation systems with insufficient observability. However, in the case of GPS failure, wrong heading information may further accelerate the divergence of the navigation solution. In this study, a method of integrating the 3D magnetic vector measurements of a magnetometer is proposed as a countermeasure for the case where the GPS fails. As the proposed method does not require attitude information for integration unlike the existing magnetic heading aiding method, it is applicable even in case of GPS failure. In addition, the existing magnetic heading aiding method utilizes only one-dimensional information in the heading direction, whereas the proposed method uses the two-dimensional attitude information of the magnetic vector, thus improving the observability of the system. To confirm the effect of the proposed method, simulation was performed for the normal operation and failure situation of GPS. The result confirmed that the proposed method improved the accuracy of the navigation solution and reduced the divergence speed of the navigation solution in the case of GPS failure, as compared with that of the existing method.

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.737-767
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• 2016

This paper concerns closed hypersurfaces of dimension $n{\geq}2$ in the hyperbolic space ${\mathbb{H}}_{\kappa}^{n+1}$ of constant sectional curvature evolving in direction of its normal vector, where the speed equals a power ${\beta}{\geq}1$ of the mean curvature. The main result is that if the initial closed, weakly h-convex hypersurface satisfies that the ratio of the biggest and smallest principal curvature at everywhere is close enough to 1, depending only on n and ${\beta}$, then under the flow this is maintained, there exists a unique, smooth solution of the flow which converges to a single point in ${\mathbb{H}}_{\kappa}^{n+1}$ in a maximal finite time, and when rescaling appropriately, the evolving hypersurfaces exponential convergence to a unit geodesic sphere of ${\mathbb{H}}_{\kappa}^{n+1}$.

• Journal of the Korean Data and Information Science Society
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• v.28 no.2
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• pp.421-433
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• 2017

The CTE (conditional tail expectation) is a useful risk management measure for a diversified investment portfolio that can be generally estimated by using a transformed univariate distribution. Hong et al. (2016) proposed a multivariate CTE based on multivariate quantile vectors, and explored its characteristics for multivariate normal distributions. Since most real financial data is not distributed symmetrically, it is problematic to apply the CTE to normal distributions. In order to obtain a multivariate CTE for various kinds of joint distributions, distribution fitting methods using copula functions are proposed in this work. Among the many copula functions, the Clayton, Frank, and Gumbel functions are considered, and the multivariate CTEs are obtained by using their generator functions and parameters. These CTEs are compared with CTEs obtained using other distribution functions. The characteristics of the multivariate CTEs are discussed, as are the properties of the distribution functions and their corresponding accuracy. Finally, conclusions are derived and presented with illustrative examples.

• Journal of the Korean Data and Information Science Society
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• v.23 no.4
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• pp.825-832
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• 2012

We propose a novel way of forecasting the market shares of several brands simultaneously in a multiplicative competitive interaction model, which uses kernel regression technique incorporated with kernel machine technique applied in support vector machines and other machine learning techniques. Traditionally, the estimations of the market share attraction model are performed via a maximum likelihood estimation procedure under the assumption that the data are drawn from a normal distribution. The proposed method is shown to be a good candidate for forecasting method of the market share attraction model when normal distribution is not assumed. We apply the proposed method to forecast the market shares of 4 Korean car brands simultaneously and represent better performances than maximum likelihood estimation procedure.

• Journal of Biomedical Engineering Research
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• v.5 no.2
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• pp.121-126
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• 1984

A new approach to texture classification for quantitative ultrasound liver diagnosis using run difference matrix was developed. The run difference matrix comprised the gray level difference along with a distances. From this run difference matrix, we defined several vectors and parameters such as DOD, DGD, DAD vector, SHP, SMO, SMG, LDE, LDEL etc.Each parameter values calculated in fatty, cirrhotic, normal and chronic hepatitic liver images were plotted in a plane and we found that RDM method was more sensitive to small structural changes than the conventional run length method and showed improved classification ability between the diseases.

• Kyungpook Mathematical Journal
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• v.63 no.2
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• pp.287-311
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• 2023

In this paper, we introduce the notion of cyclic structure Jacobi semi-symmetric real hypersurfaces in the complex hyperbolic quadric Q^m* = SO⁰_2,m/SO₂SO_m. We give a classifiction of when real hypersurfaces in the complex hyperbolic quadric Q^m* having 𝔄-principal or 𝔄-isotropic unit normal vector fields have cyclic structure Jacobi semi-symmetric tensor.